c. 1200, "to deliver from some danger; rescue from peril, bring to safety," also "prevent the death of;" also theological, "to deliver from sin or its consequences; admit to eternal life; gain salvation," from Old French sauver "keep (safe), protect, redeem," from Late Latin salvare "make safe, secure," from Latin salvus "safe" (from PIE root *sol- "whole, well-kept"). From c. 1300 as "reserve for future use, hold back, store up instead of spending;" hence "keep possession of" (late 14c.).
Save face (1898) first was used among the British community in China and is said to be from Chinese; it has not been found in Chinese, but tiu lien "to lose face" does occur. To not (do something) to save one's life is recorded from 1848. To save (one's) breath "cease talking or arguing" is from 1926.